The more content a conversation accumulates since the rules are provided, the less it weighs them into what it next generates. And the more you repeat the rules back to it, (or worse -- call it out on a violation) the more the conversation becomes about the rules and the less about the game.
These are probably engineering problems that can get improved some with other interfaces to the underlying LLM, but it's not something you can pull off with the ChatGPT/BingAssistant web interfaces as they're deployed right now.
LLMs don't struggle with arithmetic because "they can't understand anything!". They struggle with arithmetic because it's really not something that's all that well encoded in language. Self supervision means you aren't necessarily always picking up the most accurate world models. There are models of arithmetic in there. They're just wrong or faulty.